Input Output Reasoning Worksheet
How to think it through (One step, one line): Read the rule carefully: what moves (or changes) in each step? Write the list (or number) after step 1, step 2, step 3 … each on a new line. Stop at the step asked and read the answer.
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- 1.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 69 23 46 77 24 19. After step 3, what is the 6th number from the left?
- 2.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 95 36 99 23 82 67. After step 4, what is the 6th number from the left?
- 3.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 62 32 11 71 85 23. After step 2, what is the 2nd number from the left?
- 4.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 5.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 20 78 87 73 21 83. After step 3, what is the 1st number from the left?
- 6.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 17 23 16 99 55 79. After step 4, what is the 6th number from the left?
- 7.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 53 25 93 71 97 48. After step 3, what is the 1st number from the left?
- 8.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 9.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 48 64 45 72 13 63. After step 4, what is the 6th number from the left?
- 10.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 85 30 36 15 94 95. After step 2, what is the 5th number from the left?
- 11.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 33 55 71 35 73 10. After step 2, what is the 1st number from the left?
- 12.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 34 89 59 40 19 18. After step 4, what is the 5th number from the left?
- 13.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 37 41 51 21 36 89. After step 3, what is the 3rd number from the left?
- 14.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 15.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 88 36 66 69 57 38. After step 4, what is the 3rd number from the left?
- 16.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 17.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 18.A number machine multiplies a number by 2 and then takes away 5. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 19.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 16 69 45 87 99 74. After step 4, what is the 2nd number from the left?
- 20.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 62 18 33 21 22 46. After step 2, what is the 4th number from the left?
- 21.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 14 40 45 19 56 37. After step 3, what is the 3rd number from the left?
- 22.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 42 50 69 74 64 28. After step 2, what is the 4th number from the left?
- 23.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 35 51 27 48 88 92. After step 3, what is the 1st number from the left?
- 24.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 91 43 46 29 10 15. After step 2, what is the 2nd number from the left?
- 25.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 61 88 64 74 99 77. After step 2, what is the 3rd number from the left?
- 26.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 27.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 28.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 29.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 30.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 31.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 81 76 54 85 35 49. After step 3, what is the 4th number from the left?
- 32.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 33.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 87 64 96 75 23 30. After step 3, what is the 2nd number from the left?
- 34.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 88 26 71 51 85 91. After step 2, what is the 2nd number from the left?
- 35.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 36 92 40 70 13 59. After step 3, what is the 1st number from the left?
- 36.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 53 11 47 76 10 45. After step 3, what is the 5th number from the left?
- 37.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 39 15 82 94 20 75. After step 4, what is the 1st number from the left?
- 38.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 83 31 29 15 63 60. After step 3, what is the 4th number from the left?
- 39.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 40.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 76 75 46 16 71 74. After step 3, what is the 3rd number from the left?
Answer key
- 77
- 99
- 23
- 80
- 87
- 79
- 97
- 107
- 72
- 94
- 10
- 19
- 41
- 76
- 66
- 25
- 10
- 13
- 45
- 33
- 40
- 69
- 92
- 15
- 88
- 107
- 241
- 121
- 8
- 6
- 81
- 80
- 30
- 51
- 13
- 10
- 15
- 83
- 79
- 71
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